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The widely used incremental dynamic analysis (IDA) offers attractive efficiencies to organize and conduct nonlinear dynamic structural analyses under earthquake ground motions. However, its use of a fixed ground motion set limits its ability to resolve ground motion characteristics that vary based on location and intensity. To overcome this limitation and utilize IDA in site-specific seismic risk analysis, a new method is proposed, called the site-specific adjustment framework for incremental dynamic analysis (SAF-IDA), which involves two modifications to conventional IDA. The first is a process to select input ground motions for the IDA over a distributed grid of ground motion characteristics that influence structural response. The second is a post-processing procedure to develop a surrogate model from the raw IDA data to adjust the structural response results based on site- and intensity-specific ground motion hazard parameters. The proposed SAF-IDA method is illustrated in case study analyses of archetype building structures and validated through comparison with analysis results based on more computationally intensive multiple stripe analysis (MSA), which employs site-specific selection of ground motions for each intensity level.